R Code for A Justification and Application of Eigenvector Centrality

Source: http://www.r-bloggers.com/r-code-for-a-justification-and-application-of-eigenvector-centrality/?utm_source=feedburner&utm_medium=email&utm_campaign=Feed%3A+RBloggers+%28R+bloggers%29

Leo Spizzirri does an excellent job of providing mathematical intuition behind eigenvector centrality. As I was reading through it, I found it easier to just work through the matrix operations he proposes using R. You can find his paper here: https://www.math.washington.edu/~morrow/336_11/papers/leo.pdf

My R code follows. This is for the example using degree centrality which made the most sense to me. For some reason, in the last section, for very large k there is an issue with computing the vector, I think it is stemming from my definition of B_K. The same issue occurs with large k using the function MM. It could be that the values get too large for R to handle? Regardless, as pointed out on page 7, even at k = 10 that ck approaches the eigenvector.

# *-------------------------------------------------------------
# | PROGRAM NAME: R_BASIC_SNA
# | DATE: 4/9/12
# | CREATED BY: MATT BOGARD
# | DATE: 11/5/12 
# | PROJECT FILE: P:\R  Code References\SNA            
# *-------------------------------------------------------------
# | PURPOSE: COMPANION CODE TO Justification and Application of
# |  Eigenvector Centrality by Leo Spizzirri        
# |  https://www.math.washington.edu/~morrow/336_11/papers/leo.pdf
# *-------------------------------------------------------------
 
 
# specify the adjacency matrix

A <- matrix(c(0,1,0,0,0,0,
                        1,0,1,0,0,0,
                        0,1,0,1,1,1,
                        0,0,1,0,1,0,
                        0,0,1,1,0,1,
                        0,0,1,0,1,0 ),6,6, byrow= TRUE)

EV <- eigen(A) # compute eigenvalues and eigenvectors

max(EV$values)  # find the maximum eigenvalue

 
# get the eigenvector associated with the largest eigenvalue
centrality <- data.frame(EV$vectors[,1]) 

names(centrality) <- "Centrality"

print(centrality)

 
B <- A + diag(6)

EVB <- eigen(B) # compute eigenvalues and eigenvectors 

# they are the same as EV(A)

 
# define matrix M
M <- matrix(c(1,1,0,0,
                        1,1,1,0,
                        0,1,1,1,
                        0,0,1,1),4,4, byrow= TRUE)

 
# define function for B^k for matrix M   

   
MM <- function(k){
                  n <- (k-1)
                  B_K <- C
                  for (i in 1:n){
                                 B_K <- B_K%*%M
                  }
                  return(B_K)
}

 
MM(2) # M^2
MM(3) # M^3

 
# define c
 
c <- matrix(c(2,3,5,3,4,3))

 
# define c_k for matrix B
 
ck <- function(k){
                  n <- (k-2)
                  B_K <- B
                  for (i in 1:n){
                                 B_K <- B_K%*%B
                  }
                  c_k <- B_K%*%c  
                  return(c_k)
}

 
# derive EV centrality as k -> infinity
library(matrixcalc)

# k  = 5
ck(5)/frobenius.norm(ck(5))

# k  = 10
ck(10)/frobenius.norm(ck(10))

print(v0)

# k = 100
ck(100)/frobenius.norm(ck(100))

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